{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f8ba3161",
   "metadata": {},
   "source": [
    "# Input 4 Feature attribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6535c1f2",
   "metadata": {},
   "source": [
    "How to determine the importance of features? This is known as feature attribution. This notebook shows how to get feature scores in KANs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1d88fa9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 2.98e-03 | test_loss: 3.06e-03 | reg: 1.94e+00 | : 100%|█| 40/40 [00:17<00:00,  2.30it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "from sympy import *\n",
    "\n",
    "# let's construct a dataset\n",
    "f = lambda x: x[:,0]**2 + 0.3*x[:,1] + 0.1*x[:,2]**3 + 0.0*x[:,3]\n",
    "dataset = create_dataset(f, n_var=4)\n",
    "\n",
    "input_vars = [r'$x_'+str(i)+'$' for i in range(4)]\n",
    "\n",
    "model = KAN(width=[4,5,1])\n",
    "model.fit(dataset, steps=40, lamb=0.001);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c782f62",
   "metadata": {},
   "source": [
    "get feature score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2693a8c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.8882, 0.5098, 0.1094, 0.0009])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.feature_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "89d836df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 32 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(in_vars=input_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6182005a",
   "metadata": {},
   "source": [
    "prune inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cac3ea5f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "keep: [True, True, True, False]\n",
      "saving model version 0.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 27 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune_input()\n",
    "model.plot(in_vars=input_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e7eaa42",
   "metadata": {},
   "source": [
    "Let's consider a high-dimensional case. In the case of many inputs but only few are important, the users may want to prune input otherwise too many inputs make interpretable hard."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6a5b6ccf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 9.93e-03 | test loss: 1.37e-02 | reg: 5.89e+00 : 100%|██| 50/50 [08:03<00:00,  9.66s/it]\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "# let's construct a dataset\n",
    "n_var = 100\n",
    "\n",
    "def f(x):\n",
    "    y = 0\n",
    "    for i in range(n_var):\n",
    "        # exponential decay\n",
    "        y += x[:,[i]]**2*0.5**i\n",
    "    return y\n",
    "        \n",
    "dataset = create_dataset(f, n_var=n_var)\n",
    "\n",
    "input_vars = [r'$x_'+str(i)+'$' for i in range(n_var)]\n",
    "\n",
    "model = KAN(width=[n_var,10,10,1])\n",
    "model.fit(dataset, steps=50, lamb=0.001);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bf0deb1",
   "metadata": {},
   "source": [
    "Since there are 100D inputs, it's very time consuming to plot the whole diagram and hard to read anything meaningful out of the diagram. So we want to prune the network first (including pruning hidden nodes and pruning inputs) and then plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9e0b3dad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "keep: [True, True, True, True, True, True, True, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 60 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune()\n",
    "model = model.prune_input()\n",
    "model.plot(in_vars=input_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6d883067",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 44 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# manual prune inputs\n",
    "model = model.prune_input(active_inputs=[0,1,2,3,4])\n",
    "model.plot(in_vars=input_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3452ca73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 11 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# prune nodes\n",
    "model = model.prune_node()\n",
    "model.plot(in_vars=input_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42003070",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
